Inthispaper,we considerthe Drazin inverse of asumoftwomatricesandderiveadditive formulas under conditions weaker than those used in some recent papers on the subject. AsacorollarywegetthemainresultsfromthepaperofYangandLiu[H.Yang,X.Liu,The Drazininverseofthesumoftwomatricesanditsapplications,J.Comput.Appl.Math.235 (2011) 1412–1417]. As an application we give some new representations for the Drazin inverseofablockmatrix.